MATEC Web of Conferences
Volume 159, 2018The 2nd International Joint Conference on Advanced Engineering and Technology (IJCAET 2017) and International Symposium on Advanced Mechanical and Power Engineering (ISAMPE 2017)
|Number of page(s)||6|
|Published online||30 March 2018|
Adomian decomposition method for solving initial value problems in vibration models
Department of Mathematics, Faculty of Science and Technology, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta 55002, Indonesia
2 Department of Mechanical Engineering, Faculty of Science and Technology, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta 55002, Indonesia
* Corresponding author: firstname.lastname@example.org
A number of engineering problems have second-order ordinary differential equations as their mathematical models. In practice, we may have a large scale problem with a large number of degrees of freedom, which must be solved accurately. Therefore, treating the mathematical model governing the problems correctly is required in order to get an accurate solution. In this work, we use Adomian decomposition method to solve vibration models in the forms of initial value problems of second-order ordinary differential equations. However, for problems involving an external source, the Adomian decomposition method may not lead to an accurate solution if the external source is not correctly treated. In this paper, we propose a strategy to treat the external source when we implement the Adomian decomposition method to solve initial value problems of second-order ordinary differential equations. Computational results show that our strategy is indeed effective. We obtain accurate solutions to the considered problems. Note that exact solutions are often not available, so they need to be approximated using some methods, such as the Adomian decomposition method.
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
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